How do I write stderr to a file while using “tee” with a pipe?

Question

I know how to use tee to write the output (STDOUT) of aaa.sh to bbb.out, while still displaying it in the terminal:

Answer 1

why not simply:

./aaa.sh 2>&1 | tee -a log

This simply redirects stderr to stdout, so tee echoes both to log and to screen. Maybe I'm missing something, because some of the other solutions seem really complicated.

Note: Since bash version 4 you may use |& as an abbreviation for 2>&1 |:

./aaa.sh |& tee -a log